The elimination method is another useful technique for solving systems of linear equations. This method involves eliminating one variable in order to find the value of the other variable. Let's take a look at the step-by-step process:

1. Write down both equations in standard form, with all the terms arranged in order.

For example, let's solve the system of equations:

2x + 3y = 7 4x - 2y = 10

2. Choose one variable to eliminate by multiplying one or both equations with suitable coefficients. The goal is to create equal coefficients for the variable you want to eliminate when adding or subtracting the equations.

In our example, let's eliminate 'x' by multiplying the first equation by 2 and the second equation by -1:

4x + 6y = 14 -4x + 2y = -10

3. Add or subtract the equations to eliminate the chosen variable. In this case, subtract the second equation from the first:

8y = 24

4. Solve for the remaining variable. Divide both sides of the equation by 8 to get the value of 'y':

y = 3

5. Substitute the value of 'y' back into either of the original equations to solve for 'x'. Let's use the first equation:

2x + 3(3) = 7 2x + 9 = 7 2x = -2 x = -1

Hence, the solution to the system of equations is x = -1 and y = 3.

The elimination method is a powerful tool for solving systems of linear equations where the coefficients of one variable can be easily matched. However, it may not be as straightforward for more complex systems or those with fractions. In such cases, consider using an alternative method like substitution.

Remember, practice makes perfect! Keep working on solving systems of linear equations using the elimination method, and soon it will become second nature to you. Good luck!